1. Field of the Invention
The present invention relates to blind source separation problems and more particularly to estimating independent Auto Regressive (AR) processes from their sum.
2. Description of the Prior Art
A generic Blind Source Separation (BSS) problem is defined by the following: given m measurements x1, . . . ,xm obtained from n independent signals (sources) s1, . . . ,sn, estimate the original signals through n estimators ŝ1, . . . , ŝn, based on the time-series x1(xc2x7), . . . ,xm(xc2x7).
Current BSS literature addresses only the case when the number of sources is equal to the number of microphones, in example m=n. This is discussed by S. Amari in xe2x80x9cMinimum Mutual Information Blind Separationxe2x80x9d, Neural Computation, 1996, by A. J. Bell and T. J. Sejnowski in xe2x80x9cAn Information-maximization Approach To Blind Separation And Blind Deconvolutionxe2x80x9d, Neural Computation, 7:1129-1159, 1995, by J. F. Cardoso in xe2x80x9cInfomax And Maximum Likelihood For Blind Source Separationxe2x80x9d, IEEE Signal Processing Letters, 4(4):112-114, April 1997, by P. Comon in xe2x80x9cIndependent Component Analysis, A New Concept?xe2x80x9d, Signal Processing, 36(3):287-314, 1994, by C. Jutten and J. Herault in xe2x80x9cBlind Separation Of Sources, Part I: An Adaptive Algorithm Based On Neuromimetic Architecturexe2x80x9d, Signal Processing, 24(l):1-10, 1991, by B. A. Pearlmutter and L. C. Parra in xe2x80x9cA Context-sensitive Generalization Of ICAxe2x80x9d, In International Conference on Neural Information Processing, Hong Kong, 1996, by K. Torkkola in xe2x80x9cBlind Separation Of Convolved Sources Based On Information Maximizationxe2x80x9d, In IEEE Workshop on Neural Networks for Signal Processing, Kyoto, Japan 1996. The case when the number of measurements m is strictly smaller than the number of sources n is called the degenerate case.
It is an object of the present invention to reconstruct independent signals from degenerate mixtures. More specifically, it is an object of the present invention to estimate independent Auto Regressive (AR) processes from their sum.
The present invention is a system that reconstructs independent signals from degenerate mixtures. More specifically, the present invention estimates independent Auto Regressive (AR) processes from their sum. The invention addresses the identification subsystem for such a degenerate case, particularly the case of two AR processes of known finite dimension (m=1 and n=2).
The present invention includes an identification system and an estimator. A mixture signal and noise are inputted into the system and through noise separation, a near pure signal is outputted. The identification system includes an ARMA identifier, a computation of autocovariance coefficients, an initializer and a gradient descent system. The estimator includes filtering.